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Boolean algebra

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Boolean algebra

1. 1. Boolean Algebra Theory and Applications
2. 2. Learning Objectives <ul><li>Learn about Boolean expressions </li></ul><ul><li>Become aware of the basic properties of Boolean algebra </li></ul><ul><li>Explore the application of Boolean algebra in the design of electronic circuits </li></ul><ul><li>Learn the application of Boolean algebra in switching circuits </li></ul>
3. 3. Two-Element Boolean Algebra Let B = {0, 1}.
4. 5. Two-Element Boolean Algebra
5. 6. Logical Gates and Combinatorial Circuits
6. 7. Logical Gates and Combinatorial Circuits
7. 8. Logical Gates and Combinatorial Circuits
8. 9. Logical Gates and Combinatorial Circuits <ul><li>In circuitry theory, NOT, AND, and OR gates are the basic gates. Any circuit can be designed using these gates. The circuits designed depend only on the inputs, not on the output. In other words, these circuits have no memory. Also these circuits are called combinatorial circuits . </li></ul><ul><li>The symbols NOT gate, AND gate, and OR gate are also considered as basic circuit symbols, which are used to build general circuits. The word circuit instead of symbol is also used. </li></ul>
9. 10. Logical Gates and Combinatorial Circuits
10. 32. Logical Gates and Combinatorial Circuits <ul><li>The diagram in Figure 12.32 represents a circuit with more than one output. </li></ul>
11. 36. Logical Gates and Combinatorial Circuits <ul><li>A NOT gate can be implemented using a NAND gate (see Figure 12.36(a)). </li></ul><ul><li>An AND gate can be implemented using NAND gates (see Figure 12.36(b)). </li></ul><ul><li>An OR gate can be implemented using NAND gates (see Figure12.36(c)). </li></ul>
12. 37. Logical Gates and Combinatorial Circuits <ul><li>Any circuit which is designed by using NOT, AND, and OR gates can also be designed using only NAND gates. </li></ul><ul><li>Any circuit which is designed by using NOT, AND, and OR gates can also be designed using only NOR gates. </li></ul>